I am often adding new hens and rooster to my flock - they are just pet bantams. I have never had any problems.......guess I must be lucky! Here is my method:
Keep the new chicken - or chickens - in a large dog cage / crate, or similar wire cage.
In the cage put a roost, food and water. Then keep the cage in the other chickens run in the daytime, and then put it in the coop at night. (make sure the cage has shelter from strong sun or rain).
Once you hens are settled in and used to you feeding them etc, - about 1 week, then just let them out with the others.
There will be some chasing and a little fighting to see who is boss, but each little fight should be over in seconds. Then everything should be OK.
Keeping the new ones in the cage allows all the chickens too get used to each other, but keeps the new ones safe.
I found if you let new ones into you flock straight away the new ones are freaked out and will run around and are not confident, so the other chickens will pick on them more. The bigger the run and space for the chickens the better, as well as adding some things for the new ones to hide behind like the dog crate, large plant pots, logs, etc.
I recommend you put your new ones into quarantine for a time to make sure they won't have any diseases to spread to you other birds, but that's up to you.